Optical QuantumInformation Processing

An inaccurate historyAn incomplete progress reportAn unbiased vision…not

Anti-Outline• Continuous-variable systems• Atom-photon systems (cf. Kimble)• Hybrid systems (cf. Lukin)• Quantum imaging, or not• …

P. Kwiat

Photons

QuantumPhysics

QuantumCommunication

QuantumComputing

QuantumMetrolog

Photon only detected in one output.-use g(2) = 0 to test sources…

Equally likely to be transmitted orreflected -- cannot tell which:

-quantum random number generator (patented)

The Beamsplitter…

How do you prove it?

1905: Einstein proposed that lightwas really particles (for which hegot the Nobel prize!)

Photon, but just 1:-Single emitter

-atom/ion (Kimble) [hard to collect]-quantum dot (“designer atom”)

[BUT no two exactly alike…]

-Pair sources (SPDC, 4-wave mixing)-detection of signal photon --> “heralds” presence of idler photon

in well-defined mode

Resources for Photonic QuantumInformation Processing

!p

!s

!ikp

ks

ki

C

Spontaneous ParametricDownconversion

1 2

0.99999999...

P(n)

n

0.00000001...

Conditional 1-photon per mode

Well-behavedspatial modes

Resources for Photonic QuantumInformation Processing

NOT “on-demand”(multiplexed sources help)

High-quality OTScomponents ⇒>99.9% fidelity ‘gates’

Resources for Photonic QuantumInformation Processing

Detectors:-What we want

-high efficiency (at λ), low noise-fast (ideally at 100-fs scale)-photon-number resolving

-What we have now*-APDs, VLPCs, TES, SSPDs-η ~ 85-95% (visible to 1550 nm)-1 MHz - 1 GHz-can resolve up to ~10 photons

*But NOT all at once!

Resources for Photonic QuantumInformation Processing

Superconducting bolometric detectors-system efficiency (at 1550 nm) ~95%

(pushing toward 99%)-near-perfect photon-number resolution-slow-ish (0.1 - 1 µs)

A.E. Lita, A. J. Miller, andS. W. Nam, Opt. Exp. 16,3032 (2008)

#2

V-polarized

(from #2)

Maximally entangled state

(Polarization-) Entangled Source:

Tune pump polarization: Nonmax. entangled, mixed statesStable, simple Used to test QM in various undergrad labsNew ultra-bright versions, narrow bandwidth, …

Not on-demand, unwanted entanglement in other DOFs

PRL 75,4337 (1995)

Fiber-Based Sources (4-wave mixing)@ NIST, Northwestern,…

LOQC Gates

• Pairs created in fiberi.e., naturally single-mode

• Low-loss• Exploits existing telecom

infrastructure• 1550 nm or 1310 nm• Require cryogenic cooling

Chen, et al. Phys. Rev. Lett. 100, 133603 (2008).

Medic, et al. CLEO Conference 2009, paper ITuE7.

Degenerate Entanglement

F = 96%

Moore’s law for entanglement

Polarization-entangled pairs @ 2,000,000 s-1,with F ~98%, T > 96%

Re

Im

Φ(−) ∼ |HH〉 − |VV〉

F >99.5%Next main limitation: detector saturation

|Sexpt| = 2.7260 ± 0.0008(216σ in 0.8 s)

SLHV ≤ 2

|SQM, max| = 2√ 2 = 2.828|Sexpt| = 2.826 ± 0.005 165σ

OptimizedBell test:

Bell-Ineq. Tests

Opt. Exp. 13, 8951 (2005)

Now: Various testswith 2-5 photons(GHZ), withdifferent DOFs,“qudits”, etc.More to come…

Entanglement distribution (and QKD) over 144-kmlink between LaPalma and Tenerife (QIPS)

Now headinginto space…

R. Ursin, et al. Nat.Phys. 3, 481 (2007)

Entangled-Photon Quantum Cryptography

• Alice & Bob randomly measure polarization in the (HV) or the (45 -45) basis.• Discuss via a “public channel” which bases they used, but not the results.• Discard cases (50%) where they used different bases uncorrelated results.• Keep cases where they used the same basis perfectly correlated results!

• Define H ≡ “0” ≡ 45, V ≡ “1” ≡ −45. They now share a secret key.They now share a secret key.

Entanglement Advantages for QKD• Automatic randomness of key

• Longer distances accessible (since Bob knowswhen to look for a photon) [But decoy states…]

• Established methods to verify security of key

• Source can be automatically verified(even if “sold” by Evesdropper!)

• “Monogamy of entanglement”:Any leakage of info to other DOF

⇒ increased bit error rate (BER)Challenges: Source brightness/robustness to compete,e.g., with Decoy-state QKD. Fast quantum repeatersfor long distance key distribution.

Quantum Teleportation [Bennett et al. Phys. Rev. Lett. 70, 1895 (1993)] The basic idea –> transfer the (infinite) amount of informationin a qubit from Alice to Bob without sending the qubit itself. Requires Alice and Bob to share entanglement:

Remarks:• The original state is gone.• Neither Alice nor Bob know what it was.• Requires classical communication – no superluminal signaling.• Bell state analysis is hard…

E.g. Alice measures photonsC and A to be in a singletstate. Since C and A areorthogonal, and A and B areorthogonal,C and A must be identical!

Traditional Hong-Ou-Mandel: interfere two photons(from same source):

Two-Photon Interference

Coincidence Probability

Photons must beindistinguishable(& not entangled toother photons)!

Experimental TeleportationExperimental Teleportation Bouwmeester et al., Nature 390, 575 (1997)

Now demonstrated teleportation of continuous variables, energystates of ions, other degrees of freedom, 2-qubits, entanglement,…

What are the limits? How large (complex) of a system?How far? How fast? Teleport complex “process”?

Experimental results of teleporting an entanglement

But very low rate -- 6-photonexperiment: 100/60 hours

Q. Zhang et al. Nature Physics 2, 678 (2006)

Entanglement Swapping What if the unknown state is already entangled to a 4th particle?

Now these are entangled, despite thatthey have never directly interacted!

Need to distribute entanglement over longer distances (repeaters):

If we have a quantum storage device, we can wait until we have a pair from both sides.

L (1%)L (1%)Need ~100 pairsNeed ~100 pairs

Need ~20 pairsNeed ~20 pairs

Photon Entanglements

• Polarization (spin)

(Ou & Mandel, Shih & Alley, etc., etc.)

• Linear momentum(Rarity & Tapster)

• Orbital angular momentum(Zeilinger et al.)

• Time-Bin(Gisin et al., Inoue et al.)

• Energy-Time(Franson et al., Howell et al.)

• 3,4,5, high photon number (many)

Hyper-Entanglement PGK, JMO 44, 2173 (1997)

• Photons simultaneously entangled in multiple DOFs:

• Enlarged Hilbert space:

• Easy to perform quantum logic between DOFs• More efficient n-qubit transfer: T vs Tn

• New capabilities in quantum info. processing• full Bell-state analysis• “super-duper” dense coding• quantum communication with higher alphabets• remote preparation of entangled states• ???

Quantum “superdents coating”

✓1 entangled photon each to Bob and Alice✓Bob applies one of 4 U’s ➠1 of 4 Bell states;

sends photon to Alice✓Alice: BSA ➠ infer one of 4 messages

Channel cap. = log2 4= 2bits/photon_from_Bob

BA

2 bits

2 bits

Full BSA analysis“impossible” withlinear optics…

Polarization-spatial mode CNOT gate

Hyperentanglement-enhancedSuperdense Coding

Barreiro et al., Nature Physics 4, 282 (2008)

Average success probability: 95%⇒ channel capacity: 1.630(6) > 1.58(“limit” for linear optics superdensecoding, i.e., withouthyperentanglement)

What are the limits?How many bits/photon?Can the “hitchhiker”qubits be used, e.g., forerror correction?

Why Optical Quantum Computing?

• Very little/no decoherence -- photon’s don’t interact• Excellent performance with off-the-shelf optics• Very fast gates: single-qubit ~10 ps - 5 ns

two-qubit <150 ns

“Photons been very very good to me”

Why not Optical Quantum Computing?• Photon’s don’t interact -- 2-qubit gates hard• Linear approach: measurement-induced

nonlinearity• Nonlinear approach: Zeno and QND gates

Grover’s search algorithm with linear optics

- Gates: Linear optical elements- Nonscalable -- each new qubit doublesthe required number of optical elements

PGK et al., J. Mod. Opt. 47, 257 (2000)

Optical realization with single photons: A database of four elements

Grover’s Search algorithmAccuracy: ~97.5% (as of 2004)

Linear optical quantum computing

Knill, Laflamme and Milburn,Nature 409, 46 (2001)

•

•

•

•

•

•

SINGLE

PHOTONS

FAST

FEEDFORWARD

SINGLE PHOTON

DETECTION

Kok, Munro, Nemoto,

Ralph, Dowling & Milburn

SINGLE-PHOTONDETECTION

LARGE overhead requirements…(>105/gate)

qubit

A New Paradigm:Measurement-based computation

• 2004 - Nielsen’s solution: combine KLM non-deterministic gate with cluster-state model of quantum computation

Nielsen, PRL 93, 040503 (2004)

Uz(α1) Uz(α2) Uz(α3) Uz(α4)

Uz(β1) Uz(β2) Uz(β3) Uz(β4)

Uz(γ1) Uz(γ2) Uz(γ3) Uz(γ4)

conventional circuit

Raussendorf and Briegel, PRL 86, 5188 (2001)

α1 ±α2 ±α3 ±α4

β1 ±β2 ±β3 ±β4

γ1 ±γ2 ±γ3 ±γ4

cluster circuit

qubitqubit

CZ gate

qubit

CZ gateMeasurement on qubits

qubit

θ=α1 ±α2

Photons are hard to hold, but withcluster states you can build as you go…

Graph states (clusters and parity-encoding techniques)have greatly reduced the required resources and theloss-tolerance threshold for LOQC:

Resources (Bellstates, operations,etc.) for a reliableentangling gate

Acceptable lossfor a scalablearchitecture

Optical quantum computing

OQC Anti-Moore’s Law

CNOT with >95%success (KLM)

Cluster-statearchitectures areremarkablyimmune to loss.

Efficient LOQC possible if (source purity)×(detection effic.) > 2/3.

The tradeoffs between Resourcesand Loss-threshold

Present status:1-qubit gate fidelity: F >90%Few count rates: 10-1 3-pair/sThus far up to n = 6 (at very low rates)

Realization of photon cluster states Direct creation via down-conversion Interferometeric setup Simple polarizers

Grover search algorithmWalther et al., Nature 434, 169 (2005)

Need ‘on-demand’ sources,better detectors, and betterwires…

Feed-Forward ImplementationFeed-Forward Implementation

Pockels Cells:

KD*P crystals ~ 6.3 kV

Over 99 % fidelity (500:1)

Feed-ForwardTime < 150 ns !!

Fibers to detector 15nsDetector-Delay 35nsEOM-Delay 65nsLogics-Delay 7.5nsMisc. cables 20ns

~1 ns possible(w betterdetectors,integrated optics)

Prevedel, et al. Nature 445, 65 (2007)

Prevedel, et al. Nature 445, 65 (2007)

Silica-on-silicon Quantum Photonics

Quantuminterference

CNOT chip

S' = 0.990 ± 0.0

V = 0.995 ± 0.007

controlled-U gates: phase estimation, quantum chemistry..Toffoli gates: Shorʼs, error correction, fault tolerance…

• Even small quantum algorithms require large numbers of CU and Toffoli gates

Harnessing higher dimensions to reduce LOQC resources

• What if your architecture only has 2-qubit gates?

e.g., build Toffoli with 6 CNOTʼs

• Works by coherently isolating some quantum information from gate actions

Transformsqubit to qudit

How doesXa work?

1/32 1/721/4096

1/20736

7 3 15 11

chained gates new scheme

no. photons

probabilityof success

practicalcircuit

for demonstrating

Toffoli Gate

min. photons max. prob. min. photons max. prob.

What are the limits, e.g., when going for fault-tolerance…?

How to brew Really BIG Cluster-states: Percolation

Fusion success probability =1/2,above percolation threshold.⇒ get large piece of connectedcluster state with high probability

Red & Green – not connected Black - connected

From the percolated cluster it is easy tocompute measurement patterns toproduce any desired cluster circuit:

• Every photon undergoes only one Type-I gate and one single-qubit measurement• Removes requirement for photon rerouting (only requires feedforward to classicalmeasurement settings)• Initial resources can be as small as 4-photon cluster states

• Quantum continuous-variable modes ("qumodes") labeled byfrequency and polarization• Entangled by concurrent nonlinear interactions in photonic crystals• Near-ideal photon-number-resolving (nonGaussian) detection (SaeWoo Nam, NIST) enables universal quantum computing

The eigenmodes of a cavity form a naturally scaled ensemble of classically coherent modes

Carrier-envelope-phase locked mode-locked laser = optical frequency comb (106 modes oscillating in phase)

linear (one-photon) gain

Laser

... ...

John L. Hall Theodor W. Hänsch

Quantum frequency comb★ Multimode squeezing★ Multipartite entanglement

nonlinear (multiphoton) gain

Optical Parametric Oscillator

... ...

Scalable quantum computing in the optical frequency combMenicucci, Flammia, and Pfister, Phys. Rev. Lett. 101, 130501 (2008)

Classical frequency comb

Physical graph(frequency- & polarization-labeled)

Pooser and Pfister, Opt. Lett. 30, 2635 (2005)

Super-Resolution á la N00N

N=1 (classical)N=5 (N00N)

!

"

!

" /N

Super-Sensitivity!" =

!P̂

d P̂ / d" N=1 (classical)N=5 (N00N)

!

dP1/d"

!

dPN/d"

For Many SensorApplications — LIGO,Gyro, etc., — We Don’tCARE Which FringeWe’re On!

The Question for Us isIF any Given FringeMoves, With WhatResolution Can We TellThis!?How do we efficientlycreate these exoticstates? What else arethey good for?

Quantum (or not) Phase Metrology

Rarity, (1990)Ou, et al. (1990)Shih, Alley (1990)

….

6-photonSuper-Resolution

Resch,…,WhitePRL (2007)Queensland

19902-photon

Nagata,…,Takeuchi,Science (04 MAY)Hokkaido & Bristol

20074-photon

Super-sensitivity&

Super-resolution

Mitchell,…,SteinbergNature (13 MAY)

Toronto

20043, 4-photon

Super-resolution

Walther,…,ZeilingerNature (13 MAY)

Vienna

J. Howell et al.,Phys. Rev.Lett.(In Press for April)

Weak-Value-Enhanced Deflection-Detection

560 femto-radians

This is a classicalenhancement,discovered bystudying QM weakmeasurements.So what!What are the limitswhen combined, e.g.,with squeezed inputlight, or N00N states,or…?

Photons

QuantumPhysics

QuantumCommunication

QuantumComputing

QuantumMetrology

Quantum BattleSpace of Tomorrow

What good isQuantumInformation forVideo Games??